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Simplifying 20 = 5x + 7x2 Solving 20 = 5x + 7x2 Solving for variable 'x'. Reorder the terms: 20 + -5x + -7x2 = 5x + -5x + 7x2 + -7x2 Combine like terms: 5x + -5x = 0 20 + -5x + -7x2 = 0 + 7x2 + -7x2 20 + -5x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 20 + -5x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2.857142857 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 0.7142857143x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 0.7142857143x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 0.7142857143x + x2 = 0 + 2.857142857 0.7142857143x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 0.7142857143x + x2 = 2.857142857 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = 2.857142857 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = 2.857142857 + 0.1275510204 Combine like terms: 2.857142857 + 0.1275510204 = 2.9846938774 0.1275510204 + 0.7142857143x + x2 = 2.9846938774 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = 2.9846938774 Calculate the square root of the right side: 1.72762666 Break this problem into two subproblems by setting (x + 0.3571428572) equal to 1.72762666 and -1.72762666.Subproblem 1
x + 0.3571428572 = 1.72762666 Simplifying x + 0.3571428572 = 1.72762666 Reorder the terms: 0.3571428572 + x = 1.72762666 Solving 0.3571428572 + x = 1.72762666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 1.72762666 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 1.72762666 + -0.3571428572 x = 1.72762666 + -0.3571428572 Combine like terms: 1.72762666 + -0.3571428572 = 1.3704838028 x = 1.3704838028 Simplifying x = 1.3704838028Subproblem 2
x + 0.3571428572 = -1.72762666 Simplifying x + 0.3571428572 = -1.72762666 Reorder the terms: 0.3571428572 + x = -1.72762666 Solving 0.3571428572 + x = -1.72762666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -1.72762666 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -1.72762666 + -0.3571428572 x = -1.72762666 + -0.3571428572 Combine like terms: -1.72762666 + -0.3571428572 = -2.0847695172 x = -2.0847695172 Simplifying x = -2.0847695172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3704838028, -2.0847695172}
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